On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig
A conjecture from the second author’s paper [Linear Algebra Appl., 332–334 (2001) 519–531] concerning a family of polynomials is proved and strengthened. A consequence of this is that for any n ≥ 4 there is an n × n matrix that is not similar to a Toeplitz matrix, which was proved before for odd n and n = 6, 8, 10.
Mathematics Subject Classification (2000)Primary 15A21 Secondary 15A18
KeywordsToeplitz matrix Jordan normal form Inverse eigenvalue problem
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